Berkley & Gay Furniture

I am looking for information on a vanity and small chest/dresser I've had for twenty years...college days hand-me downs from an old roommate. Inside the drawer on the vanity is a brass metal stamp for Berkley & Gay Furniture, they are both painted an 'antiqued' green with painted line borders and floral motifs in 'autumnal' colors. I would love to be able to preserve them, but after several moves they are chipping and peeling and lose their paint in the breeze while you walk by them. About 15% the origional finish is gone to raw wood or basecoat paint.

It there a name for this particular pattern? What is the best way to refinish them? I hate to remove the design but it seems far past restoring. Can anyone help?